A Mass Spectrometer Problem

1. The problem statement, all variables and given/known data

The whole problem statement is a bit involved, but it starts with a figure illustrating a mass spectrometer. You have the chamber the gas you want to study is pumped into, and an anode and cathode. An electron beam ionizes the gas, and the ions are accelerated towards the cathode.

The problem says that after that, the ions go through a slit and enter another chamber with a magnetic and electric field, and those two fields accelerate them. The ions go through a second slit, and make circular tracks that depend on their mass.

I understand all that, but what I want to know is how one gets the velocity to the second slit — I understand that once an ion is in a magnetic field it gets accelerated (and I know which equations to use, at least partway — I just need to know the charge q of the ion to figure the force exerted by a given B field). So if I start with an ion at rest, zap t with an E and B field, I will get an acceleration (and per my classical E&M class I should get a helical trajectory).

But what stumps me a bit is what happens with the first chamber. Do I assume that the gas ions start from rest before being accelerated towards the first cathode? In that case the velocity to that first slit would be related to F= qionqcathode / 4πε0r2 if I remember right. Knowing the F = ma I can work out the acceleration and the velocity when it hits the first slit. Once i know the velocity to that point I just have to apply the relevant equations to get the velocity through the E and B chamber (the second one) to get the v through the second slit.

So that’s what I want to know. Do I assume the ions start from rest in the very first chamber, and go from there? I also noticed that one method of determining momentum of a particle in the electric field involves using a potential difference, which I assume would be related to the distance between the initial anode and cathode, correct? (p = √2mK = √2mV0e is the one I am thinking of).

Sorry to be so long about it. I just want to make sure I am not losing the plot.


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